Regensburg 2019 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 50: Poster: Nonlinear Systems, Patterns, Flows ..
DY 50.14: Poster
Thursday, April 4, 2019, 15:00–18:00, Poster B2
Effective Large-Scale Equations in a Model of Passive Scalar Turbulence — •Tobias Bätge1,2 and Michael Wilczek1 — 1Max-Planck-Institute for Dynamics and Self-Organization, Göttingen, Germany — 2Faculty of Physics, University of Göttingen, Germany
Turbulent flows involve dynamics across a wide range of scales. Capturing this multi-scale dynamics remains a theoretical and computational challenge. For many practical applications, a coarse-grained description of the flow is needed, in which the small scales are treated in an effective manner. How can we obtain such effective large-scale equations? Here, we address this problem at the example of a simple, one-dimensional model for the advection of a passive scalar field. Similar to the Kraichnan model, the scalar is advected by a random Gaussian field and subject to diffusion. Despite its simplicity and analytical tractability, this model shows non-trivial features such as intermittency and anomalous scaling. We propose that effective large-scale equations can be obtained by ensemble-averaging over the small-scale velocity fluctuations. We show that this procedure leads to an effective diffusivity reminiscent of phenomenological eddy viscosity models. To test our approach, we quantitatively compare the large-scale statistics of fully resolved simulations with the ones obtained from our effective large-scale equations.